Lecture 09: Data Structure Transformations. Geography 128 Analytical and Computer Cartography Spring 2007 Department of Geography University of California, Santa Barbara.
Analytical and Computer Cartography
Department of Geography
University of California, Santa Barbara
"In virtually all mapping applications it becomes necessary to convert from one cartographic data structure to another. The ability to perform these object-to-object transformations often is the single most critical determinant of a mapping system's flexibility" (Clarke, 1995)
Geocoding stamps coordinate system, resolution and projection onto objects
Data usually in generic formats at first
Can save space, gain flexibility, decrease processing time
Suit demands of analysis and modeling
Suit demands of map symbolization (e.g. fonts)Why Transform Between Structures?
Conversion of data collected at higher resolutions to lower resolution. Less data and less detail.
Simplicity -> clarity
Information will be lostGeneralization Transformations- Why Generalize?
John Krygier and Denis Wood, Making Maps:
a visual guide to map design for GIS
Centroid resolution. Less data and less detail.
Usually be seen as a part of Geocoding processGeneralization Transformations - Point-to-Point
USGS 1:250,000 3-arc second DEM format (1-degree block)
N-th Point retention resolution. Less data and less detail.
Douglas-PeuckerGeneralization Transformations - Line-to-Line Generalization
Douglas-Peucker line generalization
Splines resolution. Less data and less detail.
Trigonometric Functions (Fourier-based)Generalization Transformations - Line-to-Line Enhancement
Problem is given one set of regions, convert to another resolution. Less data and less detail.
Example: Convert census tract data to zip codes for marketing
Example: Convert crime data by police precinct to school district
May require dividing non-divisible measures, e.g population
Greatest common geographic units: Full overlap set for reassignmentGeneralization Transformations - Area-to-Area
Population at counties
Population at watersheds=?
Algorithm for Overlay resolution. Less data and less detail.
2. Chain splitting
3. Polygon reassembly
4. Labeling and attributionGeneralization Transformations - Area-to-Area
Common conversion between two major data structures, vector (TIN) and grid
Often via points and interpolation
Change cell size
Generate a new grid
Compute the intersect
Interpolate from neighboring cells
Problem of VIPsGeneralization Transformations Volume-to-Volume
Easy compared to inverse, a form of re-sampling (TIN) and grid
Grid must relate to coordinates (extent, bounds, resolution, orientation)
Rasters can be square, rectangular, hexagonal.
Resample at minimum r/2Vector-to-Raster Transformations
Convert form of vectors (e.g. to slope intercept) (TIN) and grid
Sample and convert to grid indices
Thin fat lines
Compute implicit inclusion (anti-alias)Vector-to-Raster Transformations (cnt.)- Algorithm
Much harder, more error prone. (TIN) and grid
May involve cartographer intervention
Importance of alignment
Can do points, lines, areaRaster-to-Vector Transformations
Skeletonization and Thinning (TIN) and grid
Topological ReconstructionRaster-to-Vector Transformations- Algorithm
Grid Scan (TIN) and grid
Matrix Algebra - filteringRaster-to-Vector Transformations- Edge Detection
Scale transformations are lossy (TIN) and grid
(re)storage produce error
algorithmic error, systematic and random
Types are: scale, structural (data structure), dimensional, vector-to-rasterData Structure Transformations
Kate Beard: Source error, use error, process error (TIN) and grid
Morrison: Method-produced error
Error is inherent, can it be predicted, controlled or minimized?
XT = X'
X' T^-1 = X + EThe Role of Error
Map Design (TIN) and gridNext Lecture